%%%%(c) COPYRIGHT NOTICE%FOLDUP
%%%%(c)
%%%%(c)  This file is a portion of the source for the textbook
%%%%(c)
%%%%(c)    Numerical Methods Course Notes,
%%%%(c)    Copyright 2004-2010 by Steven E. Pav
%%%%(c)
%%%%(c)  See the file COPYING.txt for copying conditions
%%%%(c)
%%%%(c)%UNFOLD

%cvs%stuff%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%FOLDUP
% $Id: sepcuts.sty 3 2005-11-08 20:56:42Z spav $
% $Log: sepcuts.sty,v $
% Revision 1.2  2005/03/17 18:11:39  spav
% minor cosmetic changes
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%UNFOLD

%%throat clearing%FOLDUP
\typeout{-- sepcuts.sty}
\typeout{-- N© 2004-2010 Steven E. Pav}
%UNFOLD

%shortcuts

\providecommand{\ahat}{\hat{a}}
\providecommand{\bhat}{\hat{b}}
\providecommand{\chat}{\hat{c}}
\providecommand{\dhat}{\hat{d}}
\providecommand{\ehat}{\hat{e}}
\providecommand{\fhat}{\hat{f}}
\providecommand{\ghat}{\hat{g}}
\providecommand{\hhat}{\hat{h}}
\providecommand{\ihat}{\hat{i}}
\providecommand{\jhat}{\hat{j}}
\providecommand{\khat}{\hat{k}}
\providecommand{\lhat}{\hat{l}}
\providecommand{\mhat}{\hat{m}}
\providecommand{\nhat}{\hat{n}}
\providecommand{\ohat}{\hat{o}}
\providecommand{\phat}{\hat{p}}
\providecommand{\qhat}{\hat{q}}
\providecommand{\rhat}{\hat{r}}
\providecommand{\shat}{\hat{s}}
\providecommand{\that}{\hat{t}}
\providecommand{\uhat}{\hat{u}}
\providecommand{\vhat}{\hat{v}}
\providecommand{\what}{\hat{w}}
\providecommand{\xhat}{\hat{x}}
\providecommand{\yhat}{\hat{y}}
\providecommand{\zhat}{\hat{z}}

\providecommand{\Ahat}{\hat{A}}
\providecommand{\Bhat}{\hat{B}}
\providecommand{\Chat}{\hat{C}}
\providecommand{\Dhat}{\hat{D}}
\providecommand{\Ehat}{\hat{E}}
\providecommand{\Fhat}{\hat{F}}
\providecommand{\Ghat}{\hat{G}}
\providecommand{\Hhat}{\hat{H}}
\providecommand{\Ihat}{\hat{I}}
\providecommand{\Jhat}{\hat{J}}
\providecommand{\Khat}{\hat{K}}
\providecommand{\Lhat}{\hat{L}}
\providecommand{\Mhat}{\hat{M}}
\providecommand{\Nhat}{\hat{N}}
\providecommand{\Ohat}{\hat{O}}
\providecommand{\Phat}{\hat{P}}
\providecommand{\Qhat}{\hat{Q}}
\providecommand{\Rhat}{\hat{R}}
\providecommand{\Shat}{\hat{S}}
\providecommand{\That}{\hat{T}}
\providecommand{\Uhat}{\hat{U}}
\providecommand{\Vhat}{\hat{V}}
\providecommand{\What}{\hat{W}}
\providecommand{\Xhat}{\hat{X}}
\providecommand{\Yhat}{\hat{Y}}
\providecommand{\Zhat}{\hat{Z}}

\providecommand{\alphahat}{\hat{\alpha}}
\providecommand{\betahat}{\hat{\beta}}
\providecommand{\gammahat}{\hat{\gamma}}
\providecommand{\deltahat}{\hat{\delta}}
\providecommand{\epsilinhat}{\hat{\epsilon}}
\providecommand{\varepsilinhat}{\hat{\varepsilon}}
\providecommand{\zetahat}{\hat{\zeta}}
\providecommand{\etahat}{\hat{\eta}}
\providecommand{\thetahat}{\hat{\theta}}
\providecommand{\varthetahat}{\hat{\vartheta}}
\providecommand{\iotahat}{\hat{\iota}}
\providecommand{\kappahat}{\hat{\kappa}}
\providecommand{\lambdahat}{\hat{\lambda}}
\providecommand{\muhat}{\hat{\mu}}
\providecommand{\nuhat}{\hat{\nu}}
\providecommand{\xihat}{\hat{\xi}}
\providecommand{\pihat}{\hat{\pi}}
\providecommand{\varpihat}{\hat{\varpi}}
\providecommand{\rhohat}{\hat{\rho}}
\providecommand{\varrhohat}{\hat{\varrho}}
\providecommand{\sigmahat}{\hat{\sigma}}
\providecommand{\varsigmahat}{\hat{\varsigma}}
\providecommand{\tauhat}{\hat{\tau}}
\providecommand{\upsilonhat}{\hat{\upsilon}}
\providecommand{\phihat}{\hat{\phi}}
\providecommand{\varphihat}{\hat{\varphi}}
\providecommand{\chihat}{\hat{\chi}}
\providecommand{\psihat}{\hat{\psi}}
\providecommand{\omegahat}{\hat{\omega}}

\providecommand{\Gammahat}{\hat{\Gamma}}
\providecommand{\Deltahat}{\hat{\Delta}}
\providecommand{\Thetahat}{\hat{\Theta}}
\providecommand{\Lambdahat}{\hat{\Lambda}}
\providecommand{\Xihat}{\hat{\Xi}}
\providecommand{\Pihat}{\hat{\Pi}}
\providecommand{\Sigmahat}{\hat{\Sigma}}
\providecommand{\Upsilonhat}{\hat{\Upsilon}}
\providecommand{\Phihat}{\hat{\Phi}}
\providecommand{\Psihat}{\hat{\Psi}}
\providecommand{\Omegahat}{\hat{\Omega}}

\providecommand{\bba}{\mathbb{a}}
\providecommand{\bbb}{\mathbb{b}}
\providecommand{\bbc}{\mathbb{c}}
\providecommand{\bbd}{\mathbb{d}}
\providecommand{\bbe}{\mathbb{e}}
\providecommand{\bbf}{\mathbb{f}}
\providecommand{\bbg}{\mathbb{g}}
\providecommand{\bbh}{\mathbb{h}}
\providecommand{\bbi}{\mathbb{i}}
\providecommand{\bbj}{\mathbb{j}}
\providecommand{\bbk}{\mathbb{k}}
\providecommand{\bbl}{\mathbb{l}}
\providecommand{\bbm}{\mathbb{m}}
\providecommand{\bbn}{\mathbb{n}}
\providecommand{\bbo}{\mathbb{o}}
\providecommand{\bbp}{\mathbb{p}}
\providecommand{\bbq}{\mathbb{q}}
\providecommand{\bbr}{\mathbb{r}}
\providecommand{\bbs}{\mathbb{s}}
\providecommand{\bbt}{\mathbb{t}}
\providecommand{\bbu}{\mathbb{u}}
\providecommand{\bbv}{\mathbb{v}}
\providecommand{\bbw}{\mathbb{w}}
\providecommand{\bbx}{\mathbb{x}}
\providecommand{\bby}{\mathbb{y}}
\providecommand{\bbz}{\mathbb{z}}

\providecommand{\bbA}{\mathbb{A}}
\providecommand{\bbB}{\mathbb{B}}
\providecommand{\bbC}{\mathbb{C}}
\providecommand{\bbD}{\mathbb{D}}
\providecommand{\bbE}{\mathbb{E}}
\providecommand{\bbF}{\mathbb{F}}
\providecommand{\bbG}{\mathbb{G}}
\providecommand{\bbH}{\mathbb{H}}
\providecommand{\bbI}{\mathbb{I}}
\providecommand{\bbJ}{\mathbb{J}}
\providecommand{\bbK}{\mathbb{K}}
\providecommand{\bbL}{\mathbb{L}}
\providecommand{\bbM}{\mathbb{M}}
\providecommand{\bbN}{\mathbb{N}}
\providecommand{\bbO}{\mathbb{O}}
\providecommand{\bbP}{\mathbb{P}}
\providecommand{\bbQ}{\mathbb{Q}}
\providecommand{\bbR}{\mathbb{R}}
\providecommand{\bbS}{\mathbb{S}}
\providecommand{\bbT}{\mathbb{T}}
\providecommand{\bbU}{\mathbb{U}}
\providecommand{\bbV}{\mathbb{V}}
\providecommand{\bbW}{\mathbb{W}}
\providecommand{\bbX}{\mathbb{X}}
\providecommand{\bbY}{\mathbb{Y}}
\providecommand{\bbZ}{\mathbb{Z}}

\providecommand{\abar}{{\bar{a}}}
\providecommand{\bbar}{{\bar{b}}}
\providecommand{\cbar}{{\bar{c}}}
\providecommand{\dbar}{{\bar{d}}}
\providecommand{\ebar}{{\bar{e}}}
\providecommand{\fbar}{{\bar{f}}}
\providecommand{\gbar}{{\bar{g}}}
\providecommand{\barh}{{\bar{h}}}
\providecommand{\ibar}{{\bar{i}}}
\providecommand{\jbar}{{\bar{j}}}
\providecommand{\kbar}{{\bar{k}}}
\providecommand{\lbar}{{\bar{l}}}
\providecommand{\mbar}{{\bar{m}}}
\providecommand{\nbar}{{\bar{n}}}
\providecommand{\obar}{{\bar{o}}}
\providecommand{\pbar}{{\bar{p}}}
\providecommand{\qbar}{{\bar{q}}}
\providecommand{\rbar}{{\bar{r}}}
\providecommand{\sbar}{{\bar{s}}}
\providecommand{\tbar}{{\bar{t}}}
\providecommand{\ubar}{{\bar{u}}}
\providecommand{\vbar}{{\bar{v}}}
\providecommand{\wbar}{{\bar{w}}}
\providecommand{\xbar}{{\bar{x}}}
\providecommand{\ybar}{{\bar{y}}}
\providecommand{\zbar}{{\bar{z}}}

\providecommand{\Abar}{{\bar{A}}}
\providecommand{\Bbar}{{\bar{B}}}
\providecommand{\Cbar}{{\bar{C}}}
\providecommand{\Dbar}{{\bar{D}}}
\providecommand{\Ebar}{{\bar{E}}}
\providecommand{\Fbar}{{\bar{F}}}
\providecommand{\Gbar}{{\bar{G}}}
\providecommand{\Hbar}{{\bar{H}}}
\providecommand{\Ibar}{{\bar{I}}}
\providecommand{\Jbar}{{\bar{J}}}
\providecommand{\Kbar}{{\bar{K}}}
\providecommand{\Lbar}{{\bar{L}}}
\providecommand{\Mbar}{{\bar{M}}}
\providecommand{\Nbar}{{\bar{N}}}
\providecommand{\Obar}{{\bar{O}}}
\providecommand{\Pbar}{{\bar{P}}}
\providecommand{\Qbar}{{\bar{Q}}}
\providecommand{\Rbar}{{\bar{R}}}
\providecommand{\Sbar}{{\bar{S}}}
\providecommand{\Tbar}{{\bar{T}}}
\providecommand{\Ubar}{{\bar{U}}}
\providecommand{\Vbar}{{\bar{V}}}
\providecommand{\Wbar}{{\bar{W}}}
\providecommand{\Xbar}{{\bar{X}}}
\providecommand{\Ybar}{{\bar{Y}}}
\providecommand{\Zbar}{{\bar{Z}}}

\providecommand{\alphabar}{\bar{\alpha}}
\providecommand{\betabar}{\bar{\beta}}
\providecommand{\gammabar}{\bar{\gamma}}
\providecommand{\deltabar}{\bar{\delta}}
\providecommand{\epsilinbar}{\bar{\epsilon}}
\providecommand{\varepsilinbar}{\bar{\varepsilon}}
\providecommand{\zetabar}{\bar{\zeta}}
\providecommand{\etabar}{\bar{\eta}}
\providecommand{\thetabar}{\bar{\theta}}
\providecommand{\varthetabar}{\bar{\vartheta}}
\providecommand{\iotabar}{\bar{\iota}}
\providecommand{\kappabar}{\bar{\kappa}}
\providecommand{\lambdabar}{\bar{\lambda}}
\providecommand{\mubar}{\bar{\mu}}
\providecommand{\nubar}{\bar{\nu}}
\providecommand{\xibar}{\bar{\xi}}
\providecommand{\pibar}{\bar{\pi}}
\providecommand{\varpibar}{\bar{\varpi}}
\providecommand{\rhobar}{\bar{\rho}}
\providecommand{\varrhobar}{\bar{\varrho}}
\providecommand{\sigmabar}{\bar{\sigma}}
\providecommand{\varsigmabar}{\bar{\varsigma}}
\providecommand{\taubar}{\bar{\tau}}
\providecommand{\upsilonbar}{\bar{\upsilon}}
\providecommand{\phibar}{\bar{\phi}}
\providecommand{\varphibar}{\bar{\varphi}}
\providecommand{\chibar}{\bar{\chi}}
\providecommand{\psibar}{\bar{\psi}}
\providecommand{\omegabar}{\bar{\omega}}
\providecommand{\nablabar}{\bar{\nabla}}

\providecommand{\Gammabar}{\bar{\Gamma}}
\providecommand{\Deltabar}{\bar{\Delta}}
\providecommand{\Thetabar}{\bar{\Theta}}
\providecommand{\Lambdabar}{\bar{\Lambda}}
\providecommand{\Xibar}{\bar{\Xi}}
\providecommand{\Pibar}{\bar{\Pi}}
\providecommand{\Sigmabar}{\bar{\Sigma}}
\providecommand{\Upsilonbar}{\bar{\Upsilon}}
\providecommand{\Phibar}{\bar{\Phi}}
\providecommand{\Psibar}{\bar{\Psi}}
\providecommand{\Omegabar}{\bar{\Omega}}

\providecommand{\at}{\tilde{a}}
\providecommand{\bt}{\tilde{b}}
\providecommand{\ct}{\tilde{c}}
\providecommand{\dt}{\tilde{d}}
\providecommand{\et}{\tilde{e}}
\providecommand{\ft}{\tilde{f}}
\providecommand{\gt}{\tilde{g}}
%\providecommand{\ht}{\tilde{h}}
%\providecommand{\it}{\tilde{i}}
\providecommand{\jt}{\tilde{j}}
\providecommand{\kt}{\tilde{k}}
\providecommand{\lt}{\tilde{l}}
\providecommand{\mt}{\tilde{m}}
\providecommand{\nt}{\tilde{n}}
\providecommand{\ot}{\tilde{o}}
\providecommand{\pt}{\tilde{p}}
\providecommand{\qt}{\tilde{q}}
\providecommand{\rt}{\tilde{r}}
\providecommand{\st}{\tilde{s}}
%\providecommand{\tt}{\tilde{t}}
\providecommand{\ut}{\tilde{u}}
\providecommand{\vt}{\tilde{v}}
\providecommand{\wt}{\tilde{w}}
\providecommand{\xt}{\tilde{x}}
\providecommand{\yt}{\tilde{y}}
\providecommand{\zt}{\tilde{z}}

\providecommand{\At}{\tilde{A}}
\providecommand{\Bt}{\tilde{B}}
\providecommand{\Ct}{\tilde{C}}
\providecommand{\Dt}{\tilde{D}}
\providecommand{\Et}{\tilde{E}}
\providecommand{\Ft}{\tilde{F}}
\providecommand{\Gt}{\tilde{G}}
\providecommand{\Ht}{\tilde{H}}
\providecommand{\It}{\tilde{I}}
\providecommand{\Jt}{\tilde{J}}
\providecommand{\Kt}{\tilde{K}}
\providecommand{\Lt}{\tilde{L}}
\providecommand{\Mt}{\tilde{M}}
\providecommand{\Nt}{\tilde{N}}
\providecommand{\Ot}{\tilde{O}}
\providecommand{\Pt}{\tilde{P}}
\providecommand{\Qt}{\tilde{Q}}
\providecommand{\Rt}{\tilde{R}}
\providecommand{\St}{\tilde{S}}
\providecommand{\Tt}{\tilde{T}}
\providecommand{\Ut}{\tilde{U}}
\providecommand{\Vt}{\tilde{V}}
\providecommand{\Wt}{\tilde{W}}
\providecommand{\Xt}{\tilde{X}}
\providecommand{\Yt}{\tilde{Y}}
\providecommand{\Zt}{\tilde{Z}}

\providecommand{\alphat}{\tilde{\alpha}}
\providecommand{\betat}{\tilde{\beta}}
\providecommand{\gammat}{\tilde{\gamma}}
\providecommand{\deltat}{\tilde{\delta}}
\providecommand{\epsilint}{\tilde{\epsilon}}
\providecommand{\varepsilint}{\tilde{\varepsilon}}
\providecommand{\zetat}{\tilde{\zeta}}
\providecommand{\etat}{\tilde{\eta}}
\providecommand{\thetat}{\tilde{\theta}}
\providecommand{\varthetat}{\tilde{\vartheta}}
\providecommand{\iotat}{\tilde{\iota}}
\providecommand{\kappat}{\tilde{\kappa}}
\providecommand{\lambdat}{\tilde{\lambda}}
\providecommand{\mut}{\tilde{\mu}}
\providecommand{\nut}{\tilde{\nu}}
\providecommand{\xit}{\tilde{\xi}}
\providecommand{\pit}{\tilde{\pi}}
\providecommand{\varpit}{\tilde{\varpi}}
\providecommand{\rhot}{\tilde{\rho}}
\providecommand{\varrhot}{\tilde{\varrho}}
\providecommand{\sigmat}{\tilde{\sigma}}
\providecommand{\varsigmat}{\tilde{\varsigma}}
\providecommand{\taut}{\tilde{\tau}}
\providecommand{\upsilont}{\tilde{\upsilon}}
\providecommand{\phit}{\tilde{\phi}}
\providecommand{\varphit}{\tilde{\varphi}}
\providecommand{\chit}{\tilde{\chi}}
\providecommand{\psit}{\tilde{\psi}}
\providecommand{\omegat}{\tilde{\omega}}

\providecommand{\Gammat}{\tilde{\Gamma}}
\providecommand{\Deltat}{\tilde{\Delta}}
\providecommand{\Thetat}{\tilde{\Theta}}
\providecommand{\Lambdat}{\tilde{\Lambda}}
\providecommand{\Xit}{\tilde{\Xi}}
\providecommand{\Pit}{\tilde{\Pi}}
\providecommand{\Sigmat}{\tilde{\Sigma}}
\providecommand{\Upsilont}{\tilde{\Upsilon}}
\providecommand{\Phit}{\tilde{\Phi}}
\providecommand{\Psit}{\tilde{\Psi}}
\providecommand{\Omegat}{\tilde{\Omega}}

\providecommand{\bfa}{{\bf a}}
\providecommand{\bfb}{{\bf b}}
\providecommand{\bfc}{{\bf c}}
\providecommand{\bfd}{{\bf d}}
\providecommand{\bfe}{{\bf e}}
\providecommand{\bff}{{\bf f}}
\providecommand{\bfg}{{\bf g}}
\providecommand{\bfh}{{\bf h}}
\providecommand{\bfi}{{\bf i}}
\providecommand{\bfj}{{\bf j}}
\providecommand{\bfk}{{\bf k}}
\providecommand{\bfl}{{\bf l}}
\providecommand{\bfm}{{\bf m}}
\providecommand{\bfn}{{\bf n}}
\providecommand{\bfo}{{\bf o}}
\providecommand{\bfp}{{\bf p}}
\providecommand{\bfq}{{\bf q}}
\providecommand{\bfr}{{\bf r}}
\providecommand{\bfs}{{\bf s}}
\providecommand{\bft}{{\bf t}}
\providecommand{\bfu}{{\bf u}}
\providecommand{\bfv}{{\bf v}}
\providecommand{\bfw}{{\bf w}}
\providecommand{\bfx}{{\bf x}}
\providecommand{\bfy}{{\bf y}}
\providecommand{\bfz}{{\bf z}}

\providecommand{\bfA}{{\bf A}}
\providecommand{\bfB}{{\bf B}}
\providecommand{\bfC}{{\bf C}}
\providecommand{\bfD}{{\bf D}}
\providecommand{\bfE}{{\bf E}}
\providecommand{\bfF}{{\bf F}}
\providecommand{\bfG}{{\bf G}}
\providecommand{\bfH}{{\bf H}}
\providecommand{\bfI}{{\bf I}}
\providecommand{\bfJ}{{\bf J}}
\providecommand{\bfK}{{\bf K}}
\providecommand{\bfL}{{\bf L}}
\providecommand{\bfM}{{\bf M}}
\providecommand{\bfN}{{\bf N}}
\providecommand{\bfO}{{\bf O}}
\providecommand{\bfP}{{\bf P}}
\providecommand{\bfQ}{{\bf Q}}
\providecommand{\bfR}{{\bf R}}
\providecommand{\bfS}{{\bf S}}
\providecommand{\bfT}{{\bf T}}
\providecommand{\bfU}{{\bf U}}
\providecommand{\bfV}{{\bf V}}
\providecommand{\bfW}{{\bf W}}
\providecommand{\bfX}{{\bf X}}
\providecommand{\bfY}{{\bf Y}}
\providecommand{\bfZ}{{\bf Z}}

\providecommand{\bfalpha}{{\mbox{\boldmath $\alpha$}}}
\providecommand{\bfbeta}{{\mbox{\boldmath $\beta$}}}
\providecommand{\bfgamma}{{\mbox{\boldmath $\gamma$}}}
\providecommand{\bfdelta}{{\mbox{\boldmath $\delta$}}}
\providecommand{\bfepsilin}{{\mbox{\boldmath $\epsilon$}}}
\providecommand{\bfvarepsilin}{{\mbox{\boldmath $\varepsilon$}}}
\providecommand{\bfzeta}{{\mbox{\boldmath $\zeta$}}}
\providecommand{\bfeta}{{\mbox{\boldmath $\eta$}}}
\providecommand{\bftheta}{{\mbox{\boldmath $\theta$}}}
\providecommand{\bfvartheta}{{\mbox{\boldmath $\vartheta$}}}
\providecommand{\bfiota}{{\mbox{\boldmath $\iota$}}}
\providecommand{\bfkappa}{{\mbox{\boldmath $\kappa$}}}
\providecommand{\bflambda}{{\mbox{\boldmath $\lambda$}}}
\providecommand{\bfmu}{{\mbox{\boldmath $\mu$}}}
\providecommand{\bfnu}{{\mbox{\boldmath $\nu$}}}
\providecommand{\bfxi}{{\mbox{\boldmath $\xi$}}}
\providecommand{\bfpi}{{\mbox{\boldmath $\pi$}}}
\providecommand{\bfvarpi}{{\mbox{\boldmath $\varpi$}}}
\providecommand{\bfrho}{{\mbox{\boldmath $\rho$}}}
\providecommand{\bfvarrho}{{\mbox{\boldmath $\varrho$}}}
\providecommand{\bfsigma}{{\mbox{\boldmath $\sigma$}}}
\providecommand{\bfvarsigma}{{\mbox{\boldmath $\varsigma$}}}
\providecommand{\bftau}{{\mbox{\boldmath $\tau$}}}
\providecommand{\bfupsilon}{{\mbox{\boldmath $\upsilon$}}}
\providecommand{\bfphi}{{\mbox{\boldmath $\phi$}}}
\providecommand{\bfvarphi}{{\mbox{\boldmath $\varphi$}}}
\providecommand{\bfchi}{{\mbox{\boldmath $\chi$}}}
\providecommand{\bfpsi}{{\mbox{\boldmath $\psi$}}}
\providecommand{\bfomega}{{\mbox{\boldmath $\omega$}}}

\providecommand{\bfGamma}{{\mbox{\boldmath $\Gamma$}}}
\providecommand{\bfDelta}{{\mbox{\boldmath $\Delta$}}}
\providecommand{\bfTheta}{{\mbox{\boldmath $\Theta$}}}
\providecommand{\bfLambda}{{\mbox{\boldmath $\Lambda$}}}
\providecommand{\bfXi}{{\mbox{\boldmath $\Xi$}}}
\providecommand{\bfPi}{{\mbox{\boldmath $\Pi$}}}
\providecommand{\bfSigma}{{\mbox{\boldmath $\Sigma$}}}
\providecommand{\bfUpsilon}{{\mbox{\boldmath $\Upsilon$}}}
\providecommand{\bfPhi}{{\mbox{\boldmath $\Phi$}}}
\providecommand{\bfPsi}{{\mbox{\boldmath $\Psi$}}}
\providecommand{\bfOmega}{{\mbox{\boldmath $\Omega$}}}

\providecommand{\adot}{\dot{a}}
\providecommand{\bdot}{\dot{b}}
\providecommand{\dotc}{\dot{c}}
\providecommand{\dotd}{\dot{d}}
\providecommand{\edot}{\dot{e}}
\providecommand{\fdot}{\dot{f}}
\providecommand{\gdot}{\dot{g}}
\providecommand{\hdot}{\dot{h}}
\providecommand{\idot}{\dot{i}}
\providecommand{\jdot}{\dot{j}}
\providecommand{\kdot}{\dot{k}}
\providecommand{\ldot}{\dot{l}}
\providecommand{\mdot}{\dot{m}}
\providecommand{\ndot}{\dot{n}}
%\providecommand{\odot}{\dot{o}}
\providecommand{\pdot}{\dot{p}}
\providecommand{\qdot}{\dot{q}}
\providecommand{\rdot}{\dot{r}}
\providecommand{\sdot}{\dot{s}}
\providecommand{\tdot}{\dot{t}}
\providecommand{\udot}{\dot{u}}
\providecommand{\vdot}{\dot{v}}
\providecommand{\wdot}{\dot{w}}
\providecommand{\xdot}{\dot{x}}
\providecommand{\ydot}{\dot{y}}
\providecommand{\zdot}{\dot{z}}

\providecommand{\Adot}{\dot{A}}
\providecommand{\Bdot}{\dot{B}}
\providecommand{\Cdot}{\dot{C}}
\providecommand{\dotD}{\dot{D}}
\providecommand{\Edot}{\dot{E}}
\providecommand{\Fdot}{\dot{F}}
\providecommand{\Gdot}{\dot{G}}
\providecommand{\Hdot}{\dot{H}}
\providecommand{\Idot}{\dot{I}}
\providecommand{\Jdot}{\dot{J}}
\providecommand{\Kdot}{\dot{K}}
\providecommand{\Ldot}{\dot{L}}
\providecommand{\Mdot}{\dot{M}}
\providecommand{\Ndot}{\dot{N}}
\providecommand{\Odot}{\dot{O}}
\providecommand{\Pdot}{\dot{P}}
\providecommand{\Qdot}{\dot{Q}}
\providecommand{\Rdot}{\dot{R}}
\providecommand{\Sdot}{\dot{S}}
\providecommand{\Tdot}{\dot{T}}
\providecommand{\Udot}{\dot{U}}
\providecommand{\Vdot}{\dot{V}}
\providecommand{\Wdot}{\dot{W}}
\providecommand{\Xdot}{\dot{X}}
\providecommand{\Ydot}{\dot{Y}}
\providecommand{\Zdot}{\dot{Z}}

\providecommand{\alphadot}{\dot{\alpha}}
\providecommand{\betadot}{\dot{\beta}}
\providecommand{\gammadot}{\dot{\gamma}}
\providecommand{\deltadot}{\dot{\delta}}
\providecommand{\epsilindot}{\dot{\epsilon}}
\providecommand{\varepsilindot}{\dot{\varepsilon}}
\providecommand{\zetadot}{\dot{\zeta}}
\providecommand{\etadot}{\dot{\eta}}
\providecommand{\thetadot}{\dot{\theta}}
\providecommand{\varthetadot}{\dot{\vartheta}}
\providecommand{\iotadot}{\dot{\iota}}
\providecommand{\kappadot}{\dot{\kappa}}
\providecommand{\lambdadot}{\dot{\lambda}}
\providecommand{\mudot}{\dot{\mu}}
\providecommand{\nudot}{\dot{\nu}}
\providecommand{\xidot}{\dot{\xi}}
\providecommand{\pidot}{\dot{\pi}}
\providecommand{\varpidot}{\dot{\varpi}}
\providecommand{\rhodot}{\dot{\rho}}
\providecommand{\varrhodot}{\dot{\varrho}}
\providecommand{\sigmadot}{\dot{\sigma}}
\providecommand{\varsigmadot}{\dot{\varsigma}}
\providecommand{\taudot}{\dot{\tau}}
\providecommand{\upsilondot}{\dot{\upsilon}}
\providecommand{\phidot}{\dot{\phi}}
\providecommand{\varphidot}{\dot{\varphi}}
\providecommand{\chidot}{\dot{\chi}}
\providecommand{\psidot}{\dot{\psi}}
\providecommand{\omegadot}{\dot{\omega}}

\providecommand{\Gammadot}{\dot{\Gamma}}
\providecommand{\Deltadot}{\dot{\Delta}}
\providecommand{\Thetadot}{\dot{\Theta}}
\providecommand{\Lambdadot}{\dot{\Lambda}}
\providecommand{\Xidot}{\dot{\Xi}}
\providecommand{\Pidot}{\dot{\Pi}}
\providecommand{\Sigmadot}{\dot{\Sigma}}
\providecommand{\Upsilondot}{\dot{\Upsilon}}
\providecommand{\Phidot}{\dot{\Phi}}
\providecommand{\Psidot}{\dot{\Psi}}
\providecommand{\Omegadot}{\dot{\Omega}}

\providecommand{\calA}{{\cal A}}
\providecommand{\calB}{{\cal B}}
\providecommand{\calC}{{\cal C}}
\providecommand{\calD}{{\cal D}}
\providecommand{\calE}{{\cal E}}
\providecommand{\calF}{{\cal F}}
\providecommand{\calG}{{\cal G}}
\providecommand{\calH}{{\cal H}}
\providecommand{\calI}{{\cal I}}
\providecommand{\calJ}{{\cal J}}
\providecommand{\calK}{{\cal K}}
\providecommand{\calL}{{\cal L}}
\providecommand{\calM}{{\cal M}}
\providecommand{\calN}{{\cal N}}
\providecommand{\calO}{{\cal O}}
\providecommand{\calP}{{\cal P}}
\providecommand{\calQ}{{\cal Q}}
\providecommand{\calR}{{\cal R}}
\providecommand{\calS}{{\cal S}}
\providecommand{\calT}{{\cal T}}
\providecommand{\calU}{{\cal U}}
\providecommand{\calV}{{\cal V}}
\providecommand{\calW}{{\cal W}}
\providecommand{\calX}{{\cal X}}
\providecommand{\calY}{{\cal Y}}
\providecommand{\calZ}{{\cal Z}}

\providecommand{\calAhat}{\hat{\cal A}}
\providecommand{\calBhat}{\hat{\cal B}}
\providecommand{\calChat}{\hat{\cal C}}
\providecommand{\calDhat}{\hat{\cal D}}
\providecommand{\calEhat}{\hat{\cal E}}
\providecommand{\calFhat}{\hat{\cal F}}
\providecommand{\calGhat}{\hat{\cal G}}
\providecommand{\calHhat}{\hat{\cal H}}
\providecommand{\calIhat}{\hat{\cal I}}
\providecommand{\calJhat}{\hat{\cal J}}
\providecommand{\calKhat}{\hat{\cal K}}
\providecommand{\calLhat}{\hat{\cal L}}
\providecommand{\calMhat}{\hat{\cal M}}
\providecommand{\calNhat}{\hat{\cal N}}
\providecommand{\calOhat}{\hat{\cal O}}
\providecommand{\calPhat}{\hat{\cal P}}
\providecommand{\calQhat}{\hat{\cal Q}}
\providecommand{\calRhat}{\hat{\cal R}}
\providecommand{\calShat}{\hat{\cal S}}
\providecommand{\calThat}{\hat{\cal T}}
\providecommand{\calUhat}{\hat{\cal U}}
\providecommand{\calVhat}{\hat{\cal V}}
\providecommand{\calWhat}{\hat{\cal W}}
\providecommand{\calXhat}{\hat{\cal X}}
\providecommand{\calYhat}{\hat{\cal Y}}
\providecommand{\calZhat}{\hat{\cal Z}}

\providecommand{\calAbar}{\bar{\cal A}}
\providecommand{\calBbar}{\bar{\cal B}}
\providecommand{\calCbar}{\bar{\cal C}}
\providecommand{\calDbar}{\bar{\cal D}}
\providecommand{\calEbar}{\bar{\cal E}}
\providecommand{\calFbar}{\bar{\cal F}}
\providecommand{\calGbar}{\bar{\cal G}}
\providecommand{\calHbar}{\bar{\cal H}}
\providecommand{\calIbar}{\bar{\cal I}}
\providecommand{\calJbar}{\bar{\cal J}}
\providecommand{\calKbar}{\bar{\cal K}}
\providecommand{\calLbar}{\bar{\cal L}}
\providecommand{\calMbar}{\bar{\cal M}}
\providecommand{\calNbar}{\bar{\cal N}}
\providecommand{\calObar}{\bar{\cal O}}
\providecommand{\calPbar}{\bar{\cal P}}
\providecommand{\calQbar}{\bar{\cal Q}}
\providecommand{\calRbar}{\bar{\cal R}}
\providecommand{\calSbar}{\bar{\cal S}}
\providecommand{\calTbar}{\bar{\cal T}}
\providecommand{\calUbar}{\bar{\cal U}}
\providecommand{\calVbar}{\bar{\cal V}}
\providecommand{\calWbar}{\bar{\cal W}}
\providecommand{\calXbar}{\bar{\cal X}}
\providecommand{\calYbar}{\bar{\cal Y}}
\providecommand{\calZbar}{\bar{\cal Z}}

\providecommand{\calAt}{\tilde{\cal A}}
\providecommand{\calBt}{\tilde{\cal B}}
\providecommand{\calCt}{\tilde{\cal C}}
\providecommand{\calDt}{\tilde{\cal D}}
\providecommand{\calEt}{\tilde{\cal E}}
\providecommand{\calFt}{\tilde{\cal F}}
\providecommand{\calGt}{\tilde{\cal G}}
\providecommand{\calHt}{\tilde{\cal H}}
\providecommand{\calIt}{\tilde{\cal I}}
\providecommand{\calJt}{\tilde{\cal J}}
\providecommand{\calKt}{\tilde{\cal K}}
\providecommand{\calLt}{\tilde{\cal L}}
\providecommand{\calMt}{\tilde{\cal M}}
\providecommand{\calNt}{\tilde{\cal N}}
\providecommand{\calOt}{\tilde{\cal O}}
\providecommand{\calPt}{\tilde{\cal P}}
\providecommand{\calQt}{\tilde{\cal Q}}
\providecommand{\calRt}{\tilde{\cal R}}
\providecommand{\calSt}{\tilde{\cal S}}
\providecommand{\calTt}{\tilde{\cal T}}
\providecommand{\calUt}{\tilde{\cal U}}
\providecommand{\calVt}{\tilde{\cal V}}
\providecommand{\calWt}{\tilde{\cal W}}
\providecommand{\calXt}{\tilde{\cal X}}
\providecommand{\calYt}{\tilde{\cal Y}}
\providecommand{\calZt}{\tilde{\cal Z}}

%for vim modeline: (do not edit)
% vim:ts=2:sw=2:tw=79:fdm=marker:fmr=FOLDUP,UNFOLD:cms=%%s:tags=tags;:syntax=tex:filetype=tex:ai:si:cin:nu:fo=croqt:cino=p0t0c5(0:
